Natural convection heat transfer in a rectangular cavity filled with a saturated porous medium with variable permeability is investigated analytically and numerically. The side walls of the cavity are heated and cooled by constant heat fluxes, while the horizontal walls are adiabatic. The governing parameters for the problem are thermal Rayleigh number, R, the aspect ratio of the cavity, A, and the variable permeability constant, c. On the basis of the Darcy–Oberbeck–Boussinesq equations, a new analytical solution is developed in the limit of a long shallow cavity. A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is conducted to assess the validity of the analytical results. It is demonstrated that, for a wide range of the governing parameters, the flow structure and the heat transfer were well predicted by the analytical solution.

分析和数值研究了填充有可变渗透率的饱和多孔介质的矩形腔体中的自然对流换热。空腔的侧壁通过恒定的热通量加热和冷却，而水平壁则是绝热的。该问题的控制参数是热瑞利数R，腔体的长径比A和可变磁导率常数c。基于Darcy-Oberbeck-Boussinesq方程，在长浅腔的极限处开发了一种新的解析解。通过求解完整的控制方程组，对同一现象进行了数值研究，以评估分析结果的有效性。结果表明，对于宽范围的控制参数，通过解析解可以很好地预测流动结构和传热。